Washington Nationals First-Place Eliminiation Scenario
Washington must win 22 more games (45 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Washington finishes in first place with 45 wins:

Team             W	L	PCT	GB
Washington       45	117	0.278	0.00
Miami            45	117	0.278	0.00
Atlanta          45	117	0.278	0.00
New York         45	117	0.278	0.00
Philadelphia     45	117	0.278	0.00

Tie breakers
Washington wins the series with Atlanta 7 games to 6
Washington wins the series with Miami 7 games to 6
Washington wins the series with New York 7 games to 6
Washington wins the series with Philadelphia 8 games to 5

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Philadelphia     32	18	112	0.640	0.0
New York         30	20	112	0.600	2.0
Atlanta          24	25	113	0.490	7.5
Washington       23	27	112	0.460	9.0
Miami            19	29	114	0.396	12.0

Next, we show how the remaining series of games plays out in the scenario:

Atlanta currently has 1 win(s) against Miami and 1 loss(es).
Atlanta wins 5 additional game(s) against Miami and loses 6.
Atlanta loses the series 6 games to 7.
Atlanta wins 1 additional game(s) against teams outside the division and loses 71.

Atlanta currently has 0 win(s) against New York and 0 loss(es).
Atlanta wins 12 additional game(s) against New York and loses 1.
Atlanta wins the series 12 games to 1.
Atlanta wins 1 additional game(s) against teams outside the division and loses 71.

Atlanta currently has 2 win(s) against Philadelphia and 1 loss(es).
Atlanta wins 0 additional game(s) against Philadelphia and loses 10.
Atlanta loses the series 2 games to 11.
Atlanta wins 1 additional game(s) against teams outside the division and loses 71.

Atlanta currently has 3 win(s) against Washington and 3 loss(es).
Atlanta wins 3 additional game(s) against Washington and loses 4.
Atlanta loses the series 6 games to 7.
Atlanta wins 1 additional game(s) against teams outside the division and loses 71.

Miami currently has 2 win(s) against New York and 4 loss(es).
Miami wins 7 additional game(s) against New York and loses 0.
Miami wins the series 9 games to 4.
Miami wins 1 additional game(s) against teams outside the division and loses 75.

Miami currently has 1 win(s) against Philadelphia and 2 loss(es).
Miami wins 8 additional game(s) against Philadelphia and loses 2.
Miami wins the series 9 games to 4.
Miami wins 1 additional game(s) against teams outside the division and loses 75.

Miami currently has 2 win(s) against Washington and 1 loss(es).
Miami wins 4 additional game(s) against Washington and loses 6.
Miami loses the series 6 games to 7.
Miami wins 1 additional game(s) against teams outside the division and loses 75.

New York currently has 3 win(s) against Philadelphia and 0 loss(es).
New York wins 10 additional game(s) against Philadelphia and loses 0.
New York wins the series 13 games to 0.
New York wins 0 additional game(s) against teams outside the division and loses 73.

New York currently has 2 win(s) against Washington and 2 loss(es).
New York wins 4 additional game(s) against Washington and loses 5.
New York loses the series 6 games to 7.
New York wins 0 additional game(s) against teams outside the division and loses 73.

Philadelphia currently has 4 win(s) against Washington and 2 loss(es).
Philadelphia wins 1 additional game(s) against Washington and loses 6.
Philadelphia loses the series 5 games to 8.
Philadelphia wins 0 additional game(s) against teams outside the division and loses 75.

# Washington Nationals' magic number
# Washington's magic number
# Nationals' magic number
# MLB Playoff Race